1. Static Equilibrium Physics 150/250 Center of Mass Types of Motion
Torque
Types of Static Equilibrium
Translational - Rotational
Conditions for Equilibrium
Center of Gravity
Free Body Diagrams 1

2. Average position of the masses
Center of Mass =
Average position of the masses
For example:
6 kg at x=5m & 7 kg at x=10m
x coordinate of center of mass =
Think of the average height of 6 monsters that are 5m high and 7 that are 10 m high 2

3. Motion of an object can be analyzed into three types
translation of the center of mass
rotation (rigid) about the center of mass
vibration (elastic) about center of mass 3

4. 4

5. Translational Acceleration is caused by the total force on the object
If the total force FTot= 0
then there is no
Translational Acceleration
(acceleration of center of mass)
acm = 0 5

6. If velocity of center of mass is initially zero it will stay zero
Thus vcm = constant
If velocity of center of mass is initially zero it will stay zero
There may be rotation or vibrational motion around center of mass 6

7. Rotational acceleration is caused by the
total turning force = TORQUE about the center of mass. 7

8. Tangential Force Radial Force8

9. Force r 9

10. Force (F) r
1 0

11. 1 1

12. Linear = Translational Angular = Rotational
Total Force = 0; Total Torque not zero
Total Force not 0; Total Torque = 0
1 2

13. angular acceleration  = 0
If the total torque Tot= 0
then there is no
Rotational Acceleration
(change of angular speed)
angular acceleration
 = 0
1 3

14. Thus angular speed  = constant If angular speed is initially zero
it will stay zero
1 4

15. There will be no vibration about center of mass
If object is RIGID
There will be no vibration about center of mass
1 5

16. Static Equilibrium for rigid objects
vcm = 0
 = 0
FTot = 0
Tot = 0
1 6

17. Equilibrium for Rigid Objects
Conditions for Static
Equilibrium for Rigid Objects

18. The center of mass of an object will not accelerate
if the total force on the object is zero
Ftot
  a  
TRANSLATIONAL
EQUILIBRIUM cm
An object will have zero angular acceleration if the
total torque on the object is zero





 

 
ROTATIONAL
EQUILIBRIUM

19. If the initial velocity of the center of mass is zero
and the initial angular velocity is zero they will
remain zero if
Ftot

thus
acm 

 thus
a 0
When this is so the object is said to be in
STATIC
EQUILIBRIUM

20. Properties of Torque 18

21. t t = = forces The torque of a force about any point on.
the line of action of that force is zero
If a body is in translational equilibrium and
the net torque is zero with respect to one point
in the body then it is zero with respect to all
points in the body . t t = =
forces
1 9

22. Center of Gravity
The position where the force of gravity acts on the object or rigidly connected objects
2 0

23. Free Body Diagrams F1 N1 N2 W1 W2 F2
2 1